Hydrogen Direct Reduction: 2D Shrinking-Core Kinetics

Process route

Furnace controls

Reduction zone temperature 850 °C

H₂ excess ratio (vs. stoichiometric) 1.5×

Pellet descent speed 1.0×

Live readouts

Avg. metallization

Residence time

0.0 s

Off-gas produced

— H₂O (steam)

Blast furnace

1.80 t

This route

0.45 t

CO₂-equivalent per tonne of steel produced

How it works

This is the 2D companion to the 3D H2-DRI shaft-furnace simulator, computed independently rather than a flattened render of the 3D scene. It keeps the exact same shrinking-core kinetics, but represents the furnace as a schematic side cross-section (not a camera view of a 3D cylinder) and adds a diagnostic the 3D version has no equivalent for: a closed-form kinetics curve of core fraction and metallization plotted directly against residence time.

Fe2O3(s) + 3 H2(g) → 2 Fe(s) + 3 H2O(g)
f(t) = max(0, 1 − k·t)         (closed-form core fraction, since df/dt = −k is constant)
X(t) = 1 − f(t)³                (metallization degree)
k(T) = A·exp(−Ea / R_gas·T)    (Arrhenius rate law)

Because the reaction-controlled shrinking-core rate law here has a constant df/dt, its solution is exactly linear in time — so instead of discretely integrating each falling pellet, the kinetics strip below the shaft draws f(t) and X(t) analytically over the full residence-time window and marks where the current residence time lands. Raising temperature increases k(T) exponentially (Arrhenius) and steepens the line; raising H₂ excess ratio raises the hydrogen partial pressure at the pellet surface with diminishing returns (saturation); raising descent speed shortens residence time, so the marker sits further left on a still-oxidized part of the curve.

Shell (rust-orange) — remaining Fe2O3/Fe3O4 oxide, drawn to scale with the shrinking core radius r_c/R = f.
Core (grey, metallic) — reduced metallic iron; shrinks as X → 1.
Kinetics strip — the closed-form f(t) (grey) and X(t) (green) curves, with a vertical marker at the smoothed residence time reading off the live metallization percentage.
CO₂ bars — the blast-furnace bar is the fixed literature baseline (~1.8 t CO2 per tonne of steel, BF-BOF route). The H2-DRI bar is mostly indirect electricity for hydrogen production and EAF melting, and rises with furnace temperature.

H2-DRI

Oxide shell (Fe2O3) Metallic core (Fe) Rising reducing gas